A Structural Obstruction Framework for the Yang–Mills Mass Gap Problem

We present a structural framework addressing the Yang–Mills mass gap problem in four-dimensional spacetime. Rather than pursuing a full constructive quantization, this work isolates and eliminates the only logically admissible channel through which massless excitations could arise. The analysis proceeds in three steps. First, the mass gap problem is reformulated as a question of structural accessibility: any zero-mass mode would require approaching a critical, scale-invariant equality channel. Second, we prove that this channel is variationally inaccessible once non-Abelian gauge constraints are enforced, due to an unavoidable deficit generated by gauge projection and curvature self-interaction. Third, we establish that even near-critical configurations are dynamically unstable, as the same structural deficit induces enhanced dissipation that repels trajectories away from the would-be massless regime. Together, these results show that masslessness is not excluded by numerical estimates but by geometric and dynamical rigidity. The mass gap therefore emerges as a structural fact of Yang–Mills theory. Any remaining work is reduced to explicit analytic or computational completion and cannot reopen the excluded channel.